This invention relates to interferometers, e.g., displacement measuring and dispersion interferometers that measure angular and linear displacements of a measurement object such as a mask stage or a wafer stage in a lithography scanner or stepper system, and also interferometers that monitor wavelength and determine intrinsic properties of gases.
Displacement measuring interferometers monitor changes in the position of a measurement object relative to a reference object based on an optical interference signal. The interferometer generates the optical interference signal by overlapping and interfering a measurement beam reflected from the measurement object with a reference beam reflected from the reference object.
In many applications, the measurement and reference beams have orthogonal polarizations and different frequencies. The different frequencies can be produced, for example, by laser Zeeman splitting, by acousto-optical modulation, or internal to the laser using birefringent elements or the like. The orthogonal polarizations allow a polarizing beam-splitter to direct the measurement and reference beams to the measurement and reference objects, respectively, and combine the reflected measurement and reference beams to form overlapping exit measurement and reference beams. The overlapping exit beams form an output beam that subsequently passes through a polarizer. The polarizer mixes polarizations of the exit measurement and reference beams to form a mixed beam. Components of the exit measurement and reference beams in the mixed beam interfere with one another so that the intensity of the mixed beam varies with the relative phase of the exit measurement and reference beams. A detector measures the time-dependent intensity of the mixed beam and generates an electrical interference signal proportional to that intensity. Because the measurement and reference beams have different frequencies, the electrical interference signal includes a xe2x80x9cheterodynexe2x80x9d signal having a beat frequency equal to the difference between the frequencies of the exit measurement and reference beams. If the lengths of the measurement and reference paths are changing relative to one another, e.g., by translating a stage that includes the measurement object, the measured beat frequency includes a Doppler shift equal to 2vnp/xcex, where v is the relative speed of the measurement and reference objects, xcex is the wavelength of the measurement and reference beams, n is the refractive index of the medium through which the light beams travel, e.g., air or vacuum, and p is the number of passes to the reference and measurement objects. Changes in the relative position of the measurement object correspond to changes in the phase of the measured interference signal, with a 2xcfx80 phase change substantially equal to a distance change in L of xcex/(np), where L is a round-trip distance change, e.g., the change in distance to and from a stage that includes the measurement object.
Unfortunately, this equality is not always exact. Many interferometers include non-linearities such as what are known as xe2x80x9ccyclic errors.xe2x80x9d The cyclic errors can be expressed as contributions to the phase and/or the intensity of the measured interference signal and have a sinusoidal dependence on phase changes associated with changes in optical path length pnL and/or on phase changes associated with other parameters. For example, there is first harmonic cyclic error in phase that has a sinusoidal dependence on (2xcfx80pnL)/xcex and there is second harmonic cyclic error in phase that has a sinusoidal dependence on 2 (2xcfx80pnL)/xcex. Higher harmonic and fractional cyclic errors may also be present.
Cyclic errors can be produced by xe2x80x9cbeam mixing,xe2x80x9d in which a portion of an input beam that nominally forms the reference beam propagates along the measurement path and/or a portion of an input beam that nominally forms the measurement beam propagates along the reference path. Such beam mixing can be caused by misalignment of interferometer with respect to polarization states of input beam, birefringence in the optical components of the interferometer, and other imperfections in the interferometer components, e.g., imperfections in a polarizing beam-splitter used to direct orthogonally polarized input beams along respective reference and measurement paths. Because of beam mixing and the resulting cyclic errors, there is not a strictly linear relation between changes in the phase of the measured interference signal and the relative optical path length pnL between the reference and measurement paths. If not compensated, cyclic errors caused by beam mixing can limit the accuracy of distance changes measured by an interferometer. Cyclic errors can also be produced by imperfections in transmissive surfaces that produce undesired multiple reflections within the interferometer and imperfections in components such as retroreflectors and/or phase retardation plates that produce undesired ellipticities and undesired rotations of planes of polarization in beams in the interferometer. For a general reference on the theoretical causes of cyclic errors, see, for example, C. W. Wu and R. D. Deslattes, xe2x80x9cAnalytical modelling of the periodic nonlinearity in heterodyne interferometry,xe2x80x9d Applied Optics, 37, 6696-6700, 1998.
In dispersion measuring applications, optical path length measurements are made at multiple wavelengths, e.g., 532 nm and 1064 nm, and are used to measure dispersion of a gas in the measurement path of the distance measuring interferometer. The dispersion measurement can be used to convert the optical path length measured by a distance measuring interferometer into a physical length. Such a conversion can be important since changes in the measured optical path length can be caused by gas turbulence and/or by a change in the average density of the gas in the measurement arm even though the physical distance to the measurement object is unchanged. In addition to the extrinsic dispersion measurement, the conversion of the optical path length to a physical length requires knowledge of an intrinsic value of the gas. The factor xcex93 is a suitable intrinsic value and is the reciprocal dispersive power of the gas for the wavelengths used in the dispersion interferometry. The factor xcex93 can be measured separately or based on literature values. Cyclic errors in the interferometer also contribute to dispersion measurements and measurements of the factor xcex93. In addition, cyclic errors can degrade interferometric measurements used to measure and/or monitor the wavelength of a beam.
The invention features an interferometry system that uses a small angular difference in the propagation directions of orthogonally polarized components of an input beam to an interferometer. The orthogonally polarized components define reference and measurement beams for the interferometer. The angular difference allows one to distinguish between the reference and measurement beam components of the input beam and facilitates the suppression of at least some of the cyclic errors caused by interferometer imperfections.
For example, birefringence in the interferometer optics, an imperfect polarizing beam-splitting surface, and/or polarization rotation by reflective surfaces in the interferometer can cause a spurious portion of the reference beam to propagate along some or all of the measurement path. Similarly, they can cause a spurious portion of the measurement beam to propagate along some or all, of the reference path. In the absence of the angular difference, at least some of the spurious beams contribute to the interferometric output signal produced after the interferometer recombines the reference and measurement beams. Such contributions complicate the interferometric signal and effectively degrade the accuracy of the measurement.
The angular difference, however, encodes the desired portion of each of the reference and measurement beams with a propagation vector that differs from its spurious portion. For example, when imperfections in the interferometer cause a spurious portion of the reference beam to propagate along the measurement beam path, that spurious portion has a propagation vector that differs from the desired portion of the measurement beam because it was originally encoded with the reference beam propagation vector.
A compensating optic (or a set of compensating optics) in the interferometry system is then used to redirect one or both of the desired portions of the reference and measurement beams to compensate for the angular difference in propagation prior to the detection of an optical interference signal. Even though a spurious beam component may overlap with the desired component at the compensating optic and be redirected by it, the spurious component will not be redirected for optimal interference at the photo-detector because it is not encoded with the correct, initial propagation vector. Thus, at the photo-detector, the desired beam components are made parallel to one another, whereas the spurious beam diverge from the desired components and each other. Because of such divergence, any optical interference signal produced by the spurious beam averages away when integrated over the spatial extent of the detector. Alternatively, spatial filtering can be used to remove the spurious beams. In any case, the cyclic error contributions to the detected interference signal are reduced.
A polarization optic may be used to produce the angular difference between orthogonally polarized components of an input beam. The polarization optic may be, for example, a birefringent prism, either alone or in combination with one or more additional optics such as a non-birefringent wedge, a Wollaston prism, or a composite optic employing a polarizing beam splitting surface such as a composite optic forming a misaligned Mach-Zehnder interferometer. The function of the polarization optic is to produce an angular difference in propagation between orthogonally polarized components of an input beam. The magnitude of the angular difference may be, for example, on the order of about 1 mrad. In preferred embodiment, the angular difference in propagation produced by the polarization optic is small enough that the orthogonally polarized components continue to overlap along nominally common portions of the reference and measurement paths, thereby permitting compact interferometer constructions. The polarization optic may be integrally attached to the interferometer or incorporated within the interferometer. Alternatively, it can be spaced from the interferometer. For example, the polarization optic may part of a laser source used to generate the input beam and/or part of an electro-optic system used to generate a heterodyne frequency shift between the orthogonally polarized components.
The compensating optic may be positioned to receive the reference and measurement beam components after the interferometer recombines them. In such cases, for example, the compensating optic may be a polarization optic complementary to the polarization optic initially producing the angular difference. Indeed, in some embodiments, the first polarization optic and the compensating, polarization optic may correspond to different regions of the same component. Alternatively, the compensating optic may be part of, or positioned within, the interferometer. For example, an interferometer optic defining one of the measurement or reference paths (e.g., a mirror) may be oriented to compensate for the angular difference, or an optic such as a wedge may be introduced into one of the measurement or reference paths and oriented to compensate for the angular difference. Furthermore, multiple, compensating optics may be used, which in combination compensate for the angular difference. Typically, the polarization optic and the compensating optic(s) correct cyclic errors associated with interferometer imperfections located between them.
In general, in one aspect, the invention features an interferometry system including an interferometer and at least one compensation optic. The interferometer is configured to receive an input beam comprising orthogonally polarized components having an angular difference in propagation direction. During operation the interferometer directs at least a portion of one of the orthogonally polarized components along a reference path to define a reference beam and at least a portion of the other of the orthogonally polarized components along a measurement path to define a measurement beam. It then recombines the reference and measurement beams to define an output beam. The at least one compensation optic is positioned and oriented to cause the reference and measurement beam components of the output beam to be substantially co-parallel. The at least one compensation optic may be formed by one or more optics. Any of such compensation optics may be part of, located within, or positioned outside of the interferometer.
In general, in another aspect, the invention features an interferometry method. The method includes the following steps: i) providing an input beam comprising orthogonally polarized components having an angular difference in propagation direction; ii) directing at least a portion of one of the orthogonally polarized components along a reference path to define a reference beam; iii) directing at least a portion of the other of the orthogonally polarized components along a measurement path to define a measurement beam; iv) combining the reference and measurement beams to form an output beam propagating along an output path; and v) causing the reference and measurement beam components of the output beam to be substantially co-parallel.
Embodiments of the invention may include any of the following advantages.
The contribution of cyclic errors to the interferometric detection signal can be reduced, thereby increasing the accuracy of the interferometric measurement. In particular, cyclic error contributions caused by birefringence in the interferometer glass, polarization rotation from a corner cube retroreflector or stage mirror, a finite extinction ratio of a polarizing beam-splitter interface, and/or ghost reflections from the surfaces and interfaces of the interferometer (e.g., wave plates) are reduced. This reduction can be especially useful in multi-axes interferometers where one input beam is used to generate multiple sets of reference and measurement beams. This is because such interferometers tend to include large path lengths in glass, whose cumulative birefringence can cause sizable cyclic errors in the interferometric detection signal if not compensated. The systems and methods described herein, however, can suppress such cyclic errors.
Notably, the cyclic errors can be reduced without completely isolating the measurement beam from the reference beam, i.e., with spatially separating the reference beam component from the measurement beam component throughout their propagation. To the contrary, the angular difference may be small enough that the orthogonally polarized components continue to overlap along nominally common portions of the reference and measurement paths. As a result, the interferometer can be made more compactly. Moreover, because the beams see common regions of the interferometer glass, the system is less sensitive to temperature gradients and non-uniformities that would otherwise affect spatially separated beams differently.
Furthermore, the interferometry systems and methods described herein can be used to provide accurate metrology and positioning measurements in microlithography and beam-writing systems.
Other features, objects, and advantages of the invention will be apparent from the following detailed description and drawings, and from the claims.